We use measurements from the South Pole Telescope ( SPT ) Sunyaev Zel ’ dovich ( SZ ) cluster survey in combination with X-ray measurements to constrain cosmological parameters .
We present a statistical method that fits for the scaling relations of the SZ and X-ray cluster observables with mass while jointly fitting for cosmology .
The method is generalizable to multiple cluster observables , and self-consistently accounts for the effects of the cluster selection and uncertainties in cluster mass calibration on the derived cosmological constraints .
We apply this method to a data set consisting of an SZ-selected catalog of 18 galaxy clusters at z > 0.3 from the first 178 deg ^ { 2 }  of the 2500 deg ^ { 2 }  SPT-SZ survey , with 14 clusters having X-ray observations from either Chandra  or XMM-Newton .
Assuming a spatially flat \Lambda CDMÂ cosmological model , we find the SPT cluster sample constrains \sigma _ { 8 } ( \Omega _ { m } / 0.25 ) ^ { 0.30 } = 0.785 \pm 0.037 .
In combination with measurements of the CMB power spectrum from the SPT and the seven-year WMAP data , the SPT cluster sample constrains \sigma _ { 8 } = 0.795 \pm 0.016 Â and \Omega _ { m } = 0.255 \pm 0.016 , a factor of 1.5 improvement on each parameter over the CMB data alone .
We consider several extensions beyond the \Lambda CDMÂ model by including the following as free parameters : the dark energy equation of state ( w ) , the sum of the neutrino masses ( \Sigma m _ { \nu } ) , the effective number of relativistic species ( N _ { \mathrm { eff } } ) , and a primordial non-Gaussianity ( f _ { NL } ) .
We find that adding the SPT cluster data significantly improves the constraints on w and \Sigma m _ { \nu } Â beyond those found when using measurements of the CMB , supernovae , baryon acoustic oscillations , and the Hubble constant .
Considering each extension independently , we best constrain w = -0.973 \pm 0.063 and the sum of neutrino masses \Sigma m _ { \nu } < 0.28 eV at 95 % confidence , a factor of 1.25 and 1.4 improvement , respectively , over the constraints without clusters .
Assuming a \Lambda CDMÂ model with a free N _ { \mathrm { eff } } Â and \Sigma m _ { \nu } , we measure N _ { \mathrm { eff } } = 3.91 \pm 0.42 and constrain \Sigma m _ { \nu } < 0.63 eV at 95 % confidence .
We also use the SPT cluster sample to constrain f _ { NL } = -192 \pm 310 , consistent with zero primordial non-Gaussianity .
Finally , we discuss the current systematic limitations due to the cluster mass calibration , and future improvements for the recently completed 2500 deg ^ { 2 } Â SPT-SZ survey .
The survey has detected \sim 500 clusters with a median redshift of \sim 0.5 and a median mass of \sim 2.3 \times 10 ^ { 14 } M _ { \odot } / h and , when combined with an improved cluster mass calibration and existing external cosmological data sets will significantly improve constraints on w .